Make him from another European country that does like to extradite with the U.S.

Other than that....

Give Catwoman the cowl from the recent comics...

Maybe add some more familiar GCPD officers...

Have the secretary at the end of The Dark Knight Rises say:

BLAKE
Here. Try my legal name.

RECEPTIONIST
Oh here it is. Have a wonderful day, Mr. Grayson.

Blake smiles, nods and exits.

Other than these small changes -- I really love this trilogy as is. Sure there are things that could be done more to my liking... But in the world of this trilogy, it all works. Bane can have the mask from the comics in the next series. Robin can appear in the next series... But this world, these characters... Were all very well done.